NMR is a technique whereby information describing an object can be obtained non-invasively. Magnetic resonance spectroscopy (MRS) provides information relating to the chemical composition of the whole object. MRI enables the density of nuclear spins to be determined at each point in an object. SI combines these techniques to provide information on the chemical composition in localized regions of the object. An example of its use is in determining the amounts of phosphorus metabolites in different regions of the human brain, allowing the diagnosis of various brain disorders.
Slichter, "Principles of Magnetic Resonance," Springer-Verlag, 1990, describes the physics underlying NMR. The use of NMR in spectroscopy is described by Saunders and Hunter, "Modern NMR Spectroscopy," Oxford University Press, 1988. Its use in imaging is described by Morris, "Nuclear Magnetic Resonance Imaging in Medicine and Biology," Clarendon Press, 1986. Brown et al., Proc. Natl. Acad. Sci. U.S.A., Vol. 79, pp. 3523-3526, 1982, describe spectroscopic imaging.
In brief, when an object contains nuclei that have non-zero spins, the nuclei are affected by magnetic fields. It is possible, by viewing the nuclei as spinning bar magnets, to treat the spin in a classical fashion. Placed in a uniform magnetic field directed along the z axis, whose direction is not aligned with the spin, of note will be three effects upon the axis of the spin's rotation. Firstly, the axis will itself rotate about the direction of the magnetic field, i.e., it will rotate in an x-y plane. That is, the spin precesses about the magnetic field. The angular velocity of the precession, .omega., is proportional to the strength of the magnetic field, B. Mathematically, the expression .omega.=.gamma.B yields the angular velocity of the spin, where .gamma. is a constant for a given type of nucleus. Secondly, the rotation axis will decay towards the direction of the magnetic field--this is T.sub.1 relaxation. Thirdly, the x-y component of the rotation axis decays to zero--this is T.sub.2 relaxation. T.sub.2 relaxation, in general, occurs more quickly than T.sub.1 relaxation.
Generally, a series of steps are taken to obtain information about localized regions of an object using NMR. The sample is placed in a strong, uniform magnetic field B.sub.0. Sufficient time is allotted such that the nuclear spins within the sample align with the field. An additional magnetic field, also along the z axis, is applied. The additional magnetic field is made to vary linearly in strength along some direction, which is assumed here for simplicity to also be the direction of the z axis. The field is known as a slice-select gradient. Hence, the extra magnetic field at a given z coordinate due to the gradient can be written zG.sub.z (for a suitable choice of the point z=0). When only the main and gradient fields are being applied, the nuclei precess about the z axis, with an angular velocity that is a function of z. This precession is called `free-precession.`
A suitably chosen radio frequency (RF) electromagnetic pulse, or combination of such pulses, is then applied. This pulse has a magnetic field component varying at the RF frequency. Therefore, each spin sees an extra magnetic field component (only the projection onto the x-y plane being important), which causes its precession to be more complex than free-precession, since its angular speed varies in time, as does the axis about which the nucleus precesses. Mathematically, the effect of an RF pulse on the spins (or, equivalently, on the magnetization of the object) is given by the Bloch equation.
It is convenient to imagine observing the behavior of the spins not as a stationary observer, with the spins precessing rapidly about the instantaneous magnetic field, but as an observer rotating about the z axis at the same frequency as the RF pulse. This is known as the rotating frame. In the rotating frame, the spins behave as if the magnetic field in the z direction is B.sub.0 +zG.sub.z -.gamma..omega..sub.rf, where .omega..sub.rf is the angular frequency of the KF pulse. If .omega..sub.rf is chosen to equal B.sub.0, then the above field is simply zG.sub.z. This is the spin's "offset from resonance," often expressed in other units, such as angular frequency units (then offset from resonance equals .gamma. zG.sub.z).
The effect of the RF pulse is described in terms of the precession of the spins at each resonant offset value in the rotating frame. If the x and y axes are defined as some constant axes in the rotating frame, a pulse would be said, for example, to be a 90.degree. pulse on a given spin if that spin's axis of rotation rotated about the x axis by 90.degree..
The RF pulse should be chosen so that the spins within a predetermined cross section or slice, which is in the x-y plane, are rotated by a given angle around an axis in the x-y plane, and that the spins outside the slice are unaffected. This is known as frequency-selective or slice-selective excitation. As described below, a signal can be picked up from this excited slice, the strength of which depends on the projection of the spins in the x-y plane. Hence frequency-selective pulses are most commonly designed to flip spins by 90.degree., since a spin initially in the z direction would be flipped by such a pulse into the x-y plane, producing the maximum signal.
This slice is then "encoded" by applying additional magnetic fields that vary linearly in directions perpendicular to the slice-select gradient, in this case, the x and y directions. These are labeled G.sub.x and G.sub.y, and are called encoding gradients. If the object is placed within a coil, an electrical signal is induced in that coil by the spins within the excited and encoded slice, and not by the spins outside the slice. This signal, or free-induction decay (FID), gives chemical and spin-density information about the slice. In general, by repeating this procedure with different encoding gradients, it is possible to obtain chemical and spin-density information about localized volumes, or voxels, within the slice.
For example, to obtain spectroscopic imaging data of an object, both of the encoding gradients, called phase-encoding gradients in this application, are applied for a finite period after the end of the pulse. After the finite period, the FID is recorded. This is repeated several times, with each of the phase-encoding gradients stepping through a range of values. Typically, each gradient might be stepped through 8 values, and hence 64 FID acquisitions would be needed.
There is a significant problem with this procedure, related to the RF pulses that are used. For example, assuming that a 90.degree. selective pulse has been used, ideally all the spins within the slice would be rotated by the pulse from the z axis to the same direction in the x-y plane, in which case they are said to be `in phase.` In practice, RF pulses behave as if they are composed of an ideal pulse followed by a period of flee-precession; the selected spins all lie in the x-y plane, but they are dispersed throughout it. Given some fixed direction in the x-y plane, each spin lies at an angle from this direction that is linearly related to the magnetic field felt by the spin which is given by the main magnetic field, B.sub.0, the spin's z coordinate, and the spin's chemical environment. This dispersion is known as a first order phase error.
The effect of the dispersion can be corrected by subsequent processing of the data, first order phase correction, which causes significant distortion of the data, typically in the baseline of the spectra. Another post-processing method for correcting this effect is ignoring the phase information in the spectra when calculating the magnitudes; this method leads to a loss in spectral resolution.
Alternatively, the phase error can be corrected by applying an additional pulse after the initial pulse, such additional pulse being designed to refocus the spins. Unfortunately, many compounds of interest, e.g., phosphorus metabolites, have a short T.sub.2 time and, therefore, produce a signal that decays rapidly. The extra time needed for the additional pulse is often unacceptably long.